Three consecutive odd integers are such that the square of the third integer is 1515 greater than greater than the sum of the squares of the first two. one solution is 33, 55, and 77. find three other consecutive odd integers that also satisfy the given conditions.
Answers
x-----------> first odd integer
x+2--------> second consecutive odd integer
x+4-------> third consecutive odd integer
we know that
(x+4)²=15+x²+(x+2)²-------> x²+8x+16=15+x²+x²+4x+4
x²+8x+16=19+2x²+4x-------> x²-4x+3
x²-4x+3=0
using a graph tool----------> to calculate the quadratic equation
see the attached figure
the solution is
x=1
x=3
the answer is
the first odd integer x is 1
the second consecutive odd integer x+2 is 3
the third consecutive odd integer x+4 is 5
Answer:
Step-by-step explanation:
Related Questions
1. which two types of clouds indicate fair weather?
a) cirrus and cumulus
b) cirrus and stratus
c) cumulus and stratus
d) cumulus and nimbostratus,
Answers
Answer:
a) cirrus and cumulus
Step-by-step explanation:
The two types of clouds that indicate fair weather are :
a) cirrus and cumulus clouds.
Cirrus clouds are usually white and predict fair to pleasant weather.
Cumulus clouds are also called fair weather clouds and look like floating cotton in the sky.
What of following best describes the expression 9(x+7)
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•this expression is a product between two factors because they are being MULTIPLIED to each other.
•this expression is has two factors, a constant and a 2-term factor. The constant is 9 and the two term factor is (x+7).
This means the answer is...
The product of a constant factor 9 and a 2-term factor x+7
I really hope this helps!
Best wishes :)
Suppose that c is the center of a circle with radius 13 in and a point p is at a distance of 32 in from
c. find an approximate value of the measure of the angle (in degrees) that is formed by the two tangent lines drawn to the circle from p. if needed, round your answer to three decimals
Answers
so this angle = 23.9695 degrees
Therefore the required angle = 2 * 23.9695 = 47.939 to 3 DP's.
MATH HELP PLEASE WILL GIVE BRAINLIEST!
This figure shows circle Z with chords AB and RS .
mAR=55°
mRB=66°
AB=8 m
RS=8 m
What is mRS ?
Enter your answer in the box.
Answers
What is the area of the trapezoid? Enter your answer in the box. in2 The figure shows a trapezoid. The parallel bases of the trapezoid are horizontal, and top base is shorter than the bottom base. Vertical line segments are drawn inside the trapezoid from the upper vertices perpendicular to the bottom base. These segments are each 18 inches and divide the trapezoid into two right triangles and a rectangle. The rectangle lies between the two triangles. The bases of the triangles and rectangle make up the bottom base of the trapezoid. The base of each triangle is 6 inches, and the base of the rectangle is 15 inches.
Answers
At=A1+A2
At is the area of the trapezoid.
A1 is the area of the right triangles.
A2 is the area of the rectangle.
2. You can find the area of the right triangles (A1) by applying the formula for calculate the area of a triangle and multiply it by 2, because both triangles have the same dimensions. Then:
A1=2(bxh/2)
b is the base (b=6 inches).
h is the height (h=18 inches).
A1=2(6 inchesx18 inches/2)
A1=2(108 inches²/2)
A1=108 inches²
3. Now, you must find the area of the rectangle by applying the following formula:
A2=bxh
b is the base of the rectangle (b=15 inches).
h is the height ot the rectangle (h=18 inches).
A2=(15 inches)(18 inches)
A2=270 inches²
4. Therefore, the area of the trapezoid (At) is:
At=A1+A2
At=108 inches²+270 inches²
At=378 inches²
Which expression is equivalent to sec^2 x cot^2 x?
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What is the value of n? Enter your answer in the box. n =
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In this case;
5 × 7 = 4(n+8)
35 = 4n + 32
4n = 3
n = 0.75
Therefore; the value of x is 0.75
Answer:
6
Step-by-step explanation:
An inequality is shown below. x + 2.5 < 20 What is the greatest value of x from the set {10.5, 12.5, 17.5, 19.5} that makes the inequality true?
A 10.5
B 12.5
C 17.5
D 19.5
Answers
Divide 5 in a ratio of 1:2:3
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[tex]\bf 5\qquad 1:2:3\qquad \cfrac{5}{1+2+3}\implies \cfrac{5}{6} \\\\\\ \stackrel{\textit{ratio of 1}}{1\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 2}}{2\left( \frac{5}{6} \right)}\qquad \stackrel{\textit{ratio of 3}}{3\left( \frac{5}{6} \right)}\qquad \implies \qquad \frac{5}{6}~:~\frac{5}{3}~:~\frac{5}{2}[/tex]
add the ratios up, and you'll get 5.
PLEASE HELP!!
Circle 1: center (8, 5) and radius 6
Circle 2: center (−2, 1) and radius 2
What transformations can be applied to Circle 1 to prove that the circles are similar?
What scale factor does the dilation from Circle 1 to Circle 2 have?
Show your work.
Answers
Two shapes are congruent if you can turn one into another using translation, rotation, and reflection.
Two shapes are similar if you rescale one them into a shape that is congruent to the other.
We can conclude from this that in euclidian geometry all circles are similar.
We can shrink the first circle to get the second one.
Scale factor would be 1/3 as circle 1 has the radius that is 3 times the radius of circle 2.
Emma is 5 years older than 6 times Beth’s age. If Emma is 29 years old what equation represents how to find Beth’s age?
Answers
To calculate Beth's age, we use the equation 29 = 6B + 5, where 29 is Emma's age, B represents Beth's age, and then solve for B, resulting in Beth being 4 years old.
To find Beth's age, we need to set up an equation based on the information provided. We know that Emma is 29 years old and that she is 5 years older than 6 times Beth's age. This relationship can be described with the equation E = 6B + 5, where E is Emma's age and B is Beth's age.
Plugging Emma's age into the equation, we get 29 = 6B + 5.
Next, we solve for B by first subtracting 5 from both sides of the equation, which gives us 24 = 6B. Then, we divide both sides by 6 to find Beth's age: B = 24 / 6.
Finding the value of B tells us that Beth is 4 years old.
Therefore, the equation is 29 = 6B + 5.
ABCD is a trapezoid with sides AB parallel to CD, where AB = 50, CD = 20. E is a point on the side AB with the property, that the segment DE divides the given trapezoid into two parts of equal area (see figure). Calculate the length AE.
Answers
One of the two shapes that DE splits the trapezoid into is a triangle. Since the two sections of the trapezoid have an equal area, this means that the area of the triangle is 1/2 of the area of the trapezoid. Using the formulas for the area of a triangle and the area of a trapezoid we get:
1/2bh = 1/2(1/2(B+b)(h))
The base of the triangle, AE, is unknown. We do know that AE + EB = 50; let x be EB. That means that AE = 50-x.
B, the "big base" of the trapezoid, is 50. b in the trapezoid, the little base, is 20. Using all of this we now have:
1/2(50-x)h = 1/2(1/2(50+20)(h))
1/2(50-x)h = 1/2(1/2(70)h)
1/2(50-x)h=1/2(35)h
Since we have multiplied by 1/2 and h on both sides, we can divide by both of them at the same time to cancel. This will give us:
(50-x)=35
Subtract 50 from both sides:
50-x=50 = 35-50
-x = -15
x = 15
This means that EB is 15; thus AE = 50-15 =35.
Ella's college professors assign homework independently from each other. ella knows that there is a 60% chance that she will have math homework tonight and a 70% chance that she will have english homework. what is the probability that she will not have math or english homework tonight? 10% 12% 42% 70%
Answers
This would be 0.3 x 0.4=0.12 or 12% chance of both occurring.
Answer:
B. 12%
Step-by-step explanation:
We have been given that Ella knows that there is a 60% chance that she will have math homework tonight and a 70% chance that she will have English homework.
Since we know that probability of not happening an event can be found by subtracting probability of happening the event from 1.
[tex]\text{P(No math homework tonight)}=1-0.6=0.4[/tex]
[tex]\text{P(No English homework tonight)}=1-0.7=0.3[/tex]
Since both events are independent so we will multiply probability of no math homework tonight by probability of no English homework to find no math or English homework tonight.
[tex]\text{P(No math or English homework tonight)}=0.4\times 0.3[/tex]
[tex]\text{P(No math or English homework tonight)}=0.12[/tex]
Converting 0.12 to percent we will get,
[tex]0.12\times 100=12\%[/tex]
Therefore, the probability that Ella will not have math or English homework tonight is 12%.
Use the standard normal table to find the z-score that corresponds to the cumulative area 0.4661. if the area is not in the table, use the entry closest to the area. if the area is halfway between two entries, use the z-score halfway between the corresponding z-scores.
Answers
When you look on a normal distribution table, you will see that the value of 0.4661 falls between z-scores of -0.08 and -0.09. Therefore, we should find the middle of those 2 numbers to get the best possible approximation. That would be -0.085 for the z-score.
The z-score at the cumulative area of 0.4661 is -0.085
How to determine the z-score?The cumulative area is given as:
0.4661
This means that:
P = 0.4661
Next, we use a standard normal table to find the z-score.
From the standard normal table of z-scores, we have:
z = -0.085 when P = 0.4661
Hence, the z-score at the cumulative area of 0.4661 is -0.085
Read more about z-scores at:
brainly.com/question/25638875
#SPJ6
can somebody tell me the area of these figures:
Answers
2) There are a number of ways to decompose the shaded area, or to construct the shaded area. We'll do the latter.
The shaded area is 1/2 of a 4x4 square plus a small triangle below the center of the "butterfly". The latter has a base of 2 and a height of 1, so an area of
.. (1/2)*2*1 = 1
The total area is 4^2/2 +1 = 9 . . . . square units
What is the simple interest on $360 borrowed for 30 months at 12.3%?
(PLEASE EXPLAIN)
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Answer is $110.70
whats the surface area of a cylinder with a base of 12in and hieght of 40in
Answers
Math help please????
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[tex]y = \frac{-4}{3} x + \frac{12}{3} [/tex]
The y intercept simplifies to 4
y-int = 4
Determine the measures of the apothem, the radius, and the perimeter of the regular octagon.
a. a = 14.4, r = 15.6, p = 96
b. a = 14.4, r = 15.6, p = 12
c. a = 15.6, r = 14.4, p = 96
d. a = 10, r = 15.6, p = 96
Answers
we know that
A) a regular Octagon has all its eight sides congruent
B) all the eight interior angles are also congruent
C) the measure of each angle = 135º
therefore
see the attached figure
∠ alfa=135°/2--------> 67.5°
AP=12/2---------> 6 units
cos (alfa)=AP/AO----------> AO=AP/cos (alfa)
AO=6/cos(67.5)---------> 15.68 units
the radius= distance AO----------> 15.68 units
radius=15.68 units
the apothem=distance OP
sin(alfa)=OP/AO---------> OP=sin(alfa)*AO
OP=sin(67.5°)*15.68-------> 14.49 units
the apothem=14.49 units
perimeter=12*8--------> 96 units
perimeter=96 units
the answers Part A), B) and C) are
apothem=14.49 units
radius=15.68 units
perimeter=96 units
therefore the option is the a.) a = 14.4, r = 15.6, p = 96
Answer:
a.) a = 14.4, r = 15.6, p = 96
Is it possible for a system to have more than one solution? Explain your answer
Answers
A garden snail traveled 1⁄40 of a mile in 1⁄2 an hour. What was the speed of the snail? 80 miles per hour
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or if you're asking the snails speed, if so it's 0.025 miles in 30 mins and 0.05 miles an hour.
How do i find the average speed for his question: "A bicycle racer rides from a starting marker at 10m/s. She then rides back along the same rout from the turnaround marker at 16m/s. What is her average speed for the whole race?",
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To find the average speed for the whole race, you just have to add the speed from a starting marker and the speed from the turnaround marker going back and divide it by 2 since there are only two speeds involved.
10 m/s + 16m/s = 26 m/s / 2 = 13 m/s
Therefore, the average speed for the whole race is 13 m/s.
pls help!!! will make brainliest!
Answers
Can someone help me and show me how to solve this?
In the figure, YX is a tangent to circle O at point X.
mXB = 52°
mXA = 104°
What is the measure of ∠XYA?
I can't remember how to solve questions like this since it's been a while. Thanks in advance.
Answers
52 /2 = 26
the answer is 26 degrees
but I'm not completely sure
A closet is in the shape of a right rectangle prism it measures 4 1/4 feet long 3 1/4 feet wide and 6 feet tall. What is the volume of the closet
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The answer is 100% 82 [tex]7/8[/tex]. I have taken the test it was correct!
Find the value of x.
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78 + 27 + x = 180
simplify:
78 + 27 + x = 180
105 + x = 180
subtract 105 from both sides
x + 105 (-105) = 180 (-105)
x = 180 - 105
x = 75° is your answer
hope this helps
Since the sum of all angles in any triangle always equals 180°, we can just subtract to find x.
180 - 27 - 78
= 153 - 78
= 75
So, the value of x is 75°.
Hope this helps!
The length of a rectangle is 1 inch less than twice the width. the area is 21 inches^2 what is the length?
Answers
Formula for area: A = 2l + 2w, where l is the length and w is the width.
Given information:
• l = 2w - 1
• A = 21 in^2
We can plug in our values accordingly and solve for w.
A = 2l + 2w
21 = 2(2w - 1) + 2w
21 = 4w - 2 + 2w
23 = 6w - 2
23 = 6w
3.83 = w
Plug 3.83 for w into 2w - 1 to find length.
2(3.83) - 1
7.66 - 1
6.66
Finally, check your work by plugging your values into the original equation.
21 = 2(6.66) + 2(3.83)
21 = 13.32 + 7.66
21 = 20.98
Answer:
The length is approximately 6.66 inches.
You want to make a scaled-down model of the statue of liberty that fits neatly on top of a pedestal with a 20 x 20 in horizontal surface. the actual statue of liberty is approximately 152 ft tall over a 40 x 40 ft base.
a.what is the scaling factor between the statue of liberty and your model? in other words, how many more times bigger is the statue of liberty than your model? show your work.
b.how tall should your model be, in inches? show your work.
Answers
we know that
[scale factor[=[model]/[actual]
the pedestal model is 20 in*20 in
the pedestal actual is 40 ft* 40 ft
then
[scale factor]=[20 in]/[40 ft] ---------->[1 in]/[2 ft]-------> scale=1/2
the answer Part A) is
the scale factor is [1 in]/[2 ft]
b.how tall should your model be, in inches?
the actual statue of liberty is approximately 152 ft tall
[scale factor]=[model]/[actual]---------> [model]=[scale factor]*[actual]
[model]=[1/2]*[152]----------> 76 in
the answer part B) is 76 in tall
The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.
Answers
Answer:
The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.
PLZ i need anwse ASAP
The figure is the net for a rectangular prism.
What is the surface area of the rectangular prism represented by the net?
Answers
Surface area is the sum of area of all the faces .
In the net diagram, we have 6 faces. So we have to find the area of each face and add them to find the surface area .
And since each face is rectangle in shape, so we will use the formula of area of rectangle, which is
[tex]Area= length*width[/tex]
So the required surface area is
[tex]A = (11*5)+(11*4)+(11*5) +(11*4)+(5*4)+(5*4)
\\
A = 55+44+55+44+20+20 =238 mm^2[/tex]
And that's the required surface area of the rectangular prism .